The following is introduction of the background of the invention.
(1) Magnetoelectric Effects
Conventional materials give the electric polarization by applying the electric field and give the magnetic polarization by applying the magnetic field. A magnetoelectric material contains a pseudoscalar field to induce the different electromagnetic response, i.e. give the magnetic polarization by applying the electric field and give the electric polarization by applying the magnetic field. For example, references[1,2,3] give the theoretical and experimental descriptions of the magnetoelectric effects attributed to its pseudoscalar field in the crystal of Cr2O3. The pseudoscalar field of Cr2O3 depends on temperature and gives a maximal value of 0.02 in [e2/h] at the temperature of 285K, where e is the electric charge and h is the Planck's constant. Therefore, the magnetoelectric effects of Cr2O3 are very weak. Many weak Magnetoelectric Effect Material like Cr2O3 are summarized in reference[3]. Reference[4] reports a mechanism that the magnetic Cr ions depart their equivalent positions in crystal by applying an electric field to generate magnetic field. Reference[3] also reports theoretical and experimental evidences of the displacement of Cr ions departing their equivalent positions, the magnetoelectric effects of which are attributed to the magnetic gradient provided by the magnetic quadrupole in the crystal. However, the origin of the magnetic quadrupole is unclear now.
Recently, the new material of topological insulator[5,6] is discovered, which gives a pseudoscalar field stronger than that of the Cr2O3 crystal by an order of 100 times[7]. The transportation of electrons inside a topological insulator is not allowed due to a topological invariance. Instead, the electrons can move on the edge, i.e. the edge state. The topological invariance may be provided by an applying field and the atomic spin-orbit interaction. Other than the topological insulator, the multiferroics [8] also provides the relative strong magnetoelectric effects. The multiferroics is usually introduced by the coupling between ferroelectric and ferromagnetic effects. The magnetoelectric effect of multiferroics, limited by the permittivity and the permeability, is not attributed to the edge state like the topological insulator. The mechanisms to provide magnetoelectric effects for these two types of materials, topological insulator and multiferroics, are clear, both in the theoretical and the experimental aspects, while the mechanism to provide the weak magnetoelectric effects of Cr2O3 is still missing.
The transportation of electron on the edge state of a topological insulator is nontrivial, that has a ballistic motion without any scattering interference and therefore without dissipation. This edge state protected by the topological invariance is very stable and free from much interference. When a topological insulator enters a superconducting state, it becomes topological superconductor, which may provide an application of topological quantum computation, to fabricate a quantum computer[5,6].
Unlike the one-dimensional structure, the 2D and 3D topological insulators are practical to be applied, which characterized by the words Z and Z2, i.e. there are four types of 3D-Z, 3D-Z2, 2D-Z, and 2D-Z2. Among that, three types of 3D-Z2, 2D-Z, and 2D-Z2 are found, except 3D-Z type. The 2D-Z type is the thin layer performing the well-known quantum Hall effect. The 3D-Z2 type is known by the topological insulators such as Bi2Se3, Bi2Te3, and Sb2Te3. The 2D-Z2 type is known by the quantum well of HgTe/CdTe[5].
The Magnetoelectric Effect Material containing a pseudoscalar field obey an unusual Maxwell equation, which is indicated by E Wilczek in[9]. Photon transportation becomes unconventional at the very place, where the pseudoscalar field performs the space- or the time-gradient. F. W. Hehl et al. have indicated that the Magnetoelectric Effect Material containing a pseudoscalar field may be applied to detect the other type of pseudoscalar field, such as dark matter. When this magnetoelectric material enters the superconducting state, the screening effect against the electromagnetic interference becomes an advantage of the detection.
(2) The Entangled State of Multiphoton Transition and the Delocalized Nuclear Exciton
The Mössbauer state is the first low-lying excited state of nucleus performing an extraordinary precision of photon energy, because the recoil of the gamma emission is taken by the whole crystal and the recoil loss of energy disappears[10]. The femto-meter nuclear size and the forbidden condition of transition give a long lifetime of the Mössbauer gamma transition with energy on the order of 10 keV. For example, the Mössbauer state of 57Fe has the 3/2 quantum number of the angular momentum and an odd parity, written by |3/2−>. The ground state of 57Fe has the 1/2 quantum number of the angular momentum and an odd parity, written by |1/2−>. The 14.4-keV gamma emission is forbidden by the same parity of the two states to give a long lifetime of 98 ns for the M1 transition. The absorption of this Mössbauer photon by the ground state from another 57Fe nucleus in the crystal provides a neV-energy resolution to identify the environmental effect affecting the nuclei. This is the well-known Mössbauer effects. The uncertainty principle predicts that a longer lifetime gives a more precise energy resolution from the emitting photon. However, the extremely high precision of Mössbauer photon is not realizable, simply because the resonant absorption by another nucleus fails. On the contrary, the short life-time of ps cannot provide the valuable energy resolution of neV but 0.1 meV. This invention does not emphasize on increasing the energy resolution, but deals with unconventional nuclear resonant absorption of the particular Mössbauer nuclei to create the nuclear exciton.
In case that the abundence of 57Fe in a pure iron crystal is 100%, the emmited Mössbauer photon can be absorbed by the neighboring 57Fe nuclei at sufficiently low temperature. Quantum mechanics predicts that we cannot identify the very position of nuclear excitation, which becomes a delocalized state of nuclear excitation (nuclear exciton), similar to the exciton in a semiconductor. The reference[9] has theoretically discussed this state of nuclear exciton.
According to the quantum electrodynamics, the probability of atomic or nuclear transition is dictated by the orbital size, the energy, the variation of angular momentum, and the parity. The E1 transition changes one quantum number of the angular momentum and the parity, while the M1 transition changes one quantum number of the angular momentum but preserves the parity. Other than the E1- and the M1-type of transitions, it is possible to emit multiple photons simultaneously, as the entangled photons. An entangled photon pair describes two photons, the degree of freedom of which is less than the total degree of freedom of two independent photons together. The entangled state is applicable for the quantum communication and the quantum computation. Here, the natural abundance of 103Rh is 100%. The ground state of 103Rh is |1/2−> and its Mössbauer state is |7/2+>. The transition between these two states gives energy of 39.8 keV, a half-life of 56.12 min and changes 3 quanta of the angular momentum. If the emission of single photon is free from the any disturbance, the energy resolution is very narrow on the order of 10−19 eV. However, the neighboring 103Rh nuclei in crystal are definitely affected by the environment to give interference more significant than the level of 10−19 eV. The resonant absorption of single photon is therefore impossible. Yao Cheng has observed the low gamma energy from the low-lying excited state of 103Rh (in form of the poly- and the single-crystal) created by the bremsstrahlung. It indicates the emission of a photon pair[11]. In fact that the natural abundance of 103Rh is 100%, the neighboring atom must be the same isotope of 103Rh. The resonant absorption of neighboring nuclei mediated by an entangled photon pair gave the delocalized nuclear excitation, i.e. nuclear exciton. This nuclear exciton contains spin but no charge. Yao Cheng, therefore, call it the nuclear spin-density wave[12].
In case that the change of angular momentum from the transition of the first low-lying excited state is not equal 1, i.e. >2 or =0, there is a possibility to emit multiple photons of entanglement and the resonant absorption by the neighboring nuclei at the ground state. The probability to emit multiple photons is dictated by the type of multipolar transitions, the abundance of identical isotope, the amount of identical isotope, and the environmental temperature. In some case, the cascade emission from a high-level excited state intermediated via the low-lying state will provide a different type of the two-photon energy-time entanglement. However, the entangled multiphoton of interest may provide a wave vector matching the crystal constant, i.e. fulfills the Bragg condition, which creates several phenomena of the superradiance, the strong coupling, and the recoilless emission. The photoelectric effect is suppressed and the nuclear resonance of identical isotope in the crystal is extremely amplified. The size of nuclear exciton is much bigger than the lattice constant that provides an extremely large magneton. The magneton of 103Rh nuclear exciton is on the order of eV/T, which is about 108 times greater than the conventional nuclear magneton[12]. By applying a magnetic field of the Gauss order, Yao Cheng has observed the reorientation of the nuclear magnetic axis, which is attributed to the enlarged magneton of the delocalized exciton state[13]. The phase transition depends on the excitation density and temperature has also been observed[14,15].
We summarize the magnetoelectric effects available from the topological insulators of the 2D-Z2 and the 3D-Z2 types and the weak Cr2O3-type materials, which are not the multiferroics.
(1) The amplitude of pseudoscalar field is smaller than 100 [e2/h]. Therefore, a good feature of insulation is required to show the magnetoelectric effects.
(2) Two types of the 3D-Z2 and the 2D-Z2 topological insulators requires low temperature to show magnetoelectric effects, such as 10K.
(3) It is impossible to transform the 3D types to 2D types just by decreasing the thickness of materials, or transform the 2D types to 3D types by increasing the thickness.
(4) It is very difficult to maintain the insulation property of the 3D-Z2 type topological insulator, such as Bi2Se3, Bi2Te3, and Sb2Te3.
Therefore, the known topological insulators have several drawbacks being inconvenient for the applications. The inventor has paid quite a lot of research, design, try and errors to achieve this applicable invention.